Middle Path table of seven-limit rank two temperaments

This table is an updated version of Table 2 of Paul Erlich's A Middle Path. The complexity is now measured a different way (which, however, is proportional to the original complexity for this table), and some temperament names have been updated.

This table comprises all possible seven-limit 2-D cases where complexity/7.65 + damage/10 < 1.

See also Middle Path table of five-limit rank two temperaments, Middle Path table of eleven-limit rank two temperaments.

Vanishing Interval's Ratios	Temperament name	TOP period	TOP generator	Mapp. of 2	Mapp. of 3	Mapp. of 5	Mapp. of 7	Cmplx	TOP Dmg	ETs
28/27, 49/48, 64/63, 256/243, 343/324...	Blacksmith	239.18	155.35	5,0	8,0	11,1	14,0	2.01	7.24	15, 25, (30), 35bc, 40b, (45bc), 50bc, (50b)...
36/35, 50/49, 126/125, 360/343, 648/625...	Diminished	298.53	197.08	4,0	7,-1	10,-1	12,-1	2.46	5.87	12, (24d), (36d), (48cdd), 56cddd, (60cddd)...
36/35, 64/63, 81/80, 256/245, 729/700...	Dominant	1195.23	495.88	1,0	2,-1	4,-4	2,2	2.47	4.77	12, (24d), 29cd, (36d), 41cd, 46ccd, (48cdd)...
36/35, 128/125, 225/224, 405/392, 729/686...	August	399.99	107.31	3,0	5,-1	7,0	9,-2	2.58	5.87	12, (24d), 33, (36d), 45cd, (48cdd), 57cd...
50/49, 64/63, 225/224, 2048/2025...	Pajara	598.45	491.88	2,0	4,-1	3,2	4,2	3.23	3.11	22, 32, 34d, (44), 46d, 54, 56d, 58dd, (64bc)...
49/48, 81/80, 245/243, 1323/1280...	Semaphore	1203.67	252.48	1,0	2,-2	4,-8	3,-1	3.48	3.67	19, 33cd, (38d), 43d, 52cd, (57dd), 62dd...
81/80, 126/125, 225/224, 3136/3125...	Meantone	1201.70	504.13	1,0	2,-1	4,-4	7,-10	3.65	1.70	19, 31, (38d), 43, 50, 55d, (57dd), (62), 67d...
50/49, 81/80, 405/392, 4000/3969...	Injera	600.89	507.28	2,0	4,-1	8,-4	9,-4	3.70	3.58	26, 38, 50d, (52c), 62d, 64c, 66bcc, 74dd...
49/48, 225/224, 525/512, 686/675...	Negri	1203.19	1078.35	1,0	-2,4	5,-3	1,2	3.76	3.19	19, 29, (38d), 47d, 48d, (57dd), (58cd)...
64/63, 126/125, 128/125, 4000/3969...	Augene	399.02	90.59*	3,0	5,-1	7,0	8,2	3.76	2.94	27, 39d, 42, 51cd, (54c), 57bc, 63cdd, 66cd...
49/48, 126/125, 875/864, 1029/1000...	Keemun	1203.19	317.84	1,0	0,6	1,5	2,3	3.85	3.19	19, 34, (38d), 53d, (57dd), 61bcdd, (68d)...
81/80, 128/125, 648/625, 2048/2025...	Catler	99.81	75.22	12,0	19,0	28,0	33,1	3.98	3.56	36, 48c, 60cd, 60c, 72cd, (72c), 84cdd, 84c...
50/49, 245/243, 250/243, 2430/2401...	Hedgehog	598.45	436.13	2,0	1,3	1,5	2,5	4.09	3.11	22, 36c, (44), 52bdd, 58c, (66d), (72cc)...
64/63, 245/243, 1728/1715, 2240/2187...	Superpyth	1197.60	708.17	1,0	1,1	-3,9	4,-2	4.48	2.40	22, 27, (44), 49, (54c), (66d), 71d, 76bcd...
126/125, 245/243, 686/675, 4375/4374	Sensi	1198.39	755.23	1,0	6,-7	8,-9	11,-13	4.49	1.61	19, 27, (38d), 46, (54c), (57dd), 65, 73, 76dd...
50/49, 525/512, 1029/1024, 1875/1792...	Lemba	601.70	230.87	2,0	2,3	5,-1	6,-1	4.54	3.74	26, (52c), 62c, (78bcc), 88cc, 104bcc...
64/63, 250/243, 875/864, 6144/6125...	Porcupine	1196.91	1034.59	1,0	-1,3	-2,5	8,-6	4.59	3.09	22, 37, (44), 59, (66d), (74b), 81bd, (88bd)...
81/80, 525/512, 875/864, 4375/4374...	Flattone	1202.54	507.14	1,0	2,-1	4,-4	-1,9	4.77	2.54	26, 45, (52c), 64cd, 71bc, (78bcc), 83bcdd...
225/224, 245/243, 875/864, 3125/3072...	Magic	1201.28	380.80	1,0	0,5	2,1	-1,12	4.82	1.28	22, 41, (44), 60, 63, (66d), 79d, (82), 85...
50/49, 875/864, 1728/1715, 3125/3024...	Doublewide	599.28	326.96	2,0	1,4	3,3	4,3	4.84	3.27	22, (44), 48, (66d), 70c, 74c, (88bd), 92cd...
49/48, 250/243, 4000/3969, 6125/5832...	Nautilus	1202.99	1119.69	1,0	-4,6	-7,10	0,3	4.85	3.48	29, (58cd), (87ccdd), (116ccddd)...
64/63, 686/675, 2401/2400, 6272/6075...	Beatles	1197.10	842.38	1,0	3,-2	-4,9	0,4	5.24	2.90	27, (54c), (81bcd), (108bccd), 118bccd...
81/80, 686/675, 1029/1000, 10976/10935...	Liese	1202.62	569.05	1,0	3,-3	8,-12	8,-11	5.43	2.62	[almost 19], 74d, 93dd, 112bdd, 129dd...
81/80, 1029/1024, 1728/1715, 8748/8575...	Cynder	1201.7	969.18	1,0	4,-3	12,-12	2,1	5.72	1.70	31, 57, (62), 88, (93), 98, (114bc), 119b...
225/224, 1728/1715, 2430/2401, 6144/6125...	Orwell	1199.53	271.49	1,0	0,7	3,-3	1,8	6.20	0.95	31, 53, (62), 75, 84, (93), (106), 115, (124b)...
225/224, 3125/3087, 4000/3969, 5120/5103...	Garibaldi	1200.76	702.64	1,0	1,1	7,-8	11,-14	6.30	0.91	41, 53, (82), 94, (106), 118d, (123c), 135, 147...
126/125, 1728/1715, 2401/2400, 31104/30625...	Myna	1198.83	888.94	1,0	9,-10	9,-9	8,-7	6.31	1.17	58, 89, (116c), 120, 143cd, 147c, 151, 174cd...
225/224, 1029/1024, 2401/2400, 16875/16807...	Miracle	1200.63	116.72	1,0	1,6	3,-7	3,-2	6.55	0.63	41, 72, (82), 103, 113, (123c), 134, (144)...
A BONUS TEMPERAMENT:
2401/2400, 4375/4374, 250047/250000...	Ennealimmal	133.337	84.313	9,0	13,2	19,3	24,2	12.36	0.04

• Correction from the Xenharmonikon version, which gives the corner case generator 92.46 erroneously.

ET (* = contorted)	TOP damage	TOP octave	Rank-2 temperaments supported
12			diminished, dominant, august
15			blacksmith
19			semaphore, meantone, negri, keemun, sensi
22			pajara, hedgehog, superpyth, porcupine, magic, doublewide
24d*			diminished, dominant, august
25			blacksmith
26			injera, lemba, flattone
27			augene, superpyth, sensi, beatles
29			negri, nautilus
29cd			dominant
30*			blacksmith
31			meantone, cynder, orwell
32			pajara
33			august
33cd			semaphore
34			keemun
34d			pajara
35bc			blacksmith
36			catler
36c			hedgehog
36d*			diminished, dominant, august
37			porcupine
38			injera
38d*			semaphore, meantone, negri, keemun, sensi
39d			augene
40b			blacksmith
41			magic, garibaldi, miracle
41cd			dominant
42			augene
43			meantone
43d			semaphore
44*			pajara, hedgehog, superpyth, porcupine, magic, doublewide
45			flattone
45bc			blacksmith
45cd			august
46			sensi
46ccd			dominant
46d			pajara
47d			negri
48			doublewide
48c			catler
48cdd*			diminished, dominant, august
48d			negri
49			superpyth
50			meantone
50b*			blacksmith
50bc			blacksmith
50d			injera
51cd			augene
52bdd			hedgehog
52c*			injera, lemba, flattone
52cd			semaphore
53			orwell, garibaldi
53cdd			dominant
53d			keemun
54			pajara
54c*			augene, superpyth, sensi, beatles
55b			blacksmith
55d			meantone
56cddd			diminished
56d			pajara
57			cynder
57bc			augene
57cd			august
57dd*			semaphore, meantone, negri, keemun, sensi
58			myna
58c			hedgehog
58ccdd*			dominant
58cd*			negri, nautilus
58dd			pajara
59			porcupine
60			magic
60b			blacksmith
60bc*			blacksmith
60c			catler
60cd			catler
60cddd*			diminished, dominant, august

The bubble chart above (source) arranges the temperaments by complexity (x-axis) vs. damage (y-axis). Colors are arbitrary. The size of the bubble is proportional to (complexity*damage). Note that the "bonus temperament" Ennealimmal is not shown (a much larger range would be needed to make it visible).


The same chart, only "zoomed in".